Collocation and finite difference-collocation methods for the solution of nonlinear Klein-Gordon equation

Computer Physics Communications

Volumn 181, Issue 8, 2010, Pages 1392-1401

  Lakestani, Mehrdad ^a   Dehghan, Mehdi ^b  

^a UNIVERSITY OF TABRIZ   (Iran)

^b AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Cubic B spline function; Nonlinear Klein Gordon; Operational matrix of derivative

Indexed keywords

ALGEBRAIC EQUATIONS; COLLOCATION METHOD; CUBIC B -SPLINE; CUBIC B-SPLINE FUNCTION; FINITE DIFFERENCE; ILLUSTRATIVE EXAMPLES; KLEIN-GORDON; NONLINEAR KLEIN-GORDON EQUATION; NUMERICAL TECHNIQUES; OPERATIONAL MATRICES; OPERATIONAL MATRIX OF DERIVATIVE;

DIFFERENCE EQUATIONS; INTERPOLATION; MATRIX ALGEBRA; NUMERICAL METHODS; SPLINES;

NONLINEAR EQUATIONS;

EID: 77953140249     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2010.04.006     Document Type: Article

References (41)

1. Bratsos A.G., and Twizell E.H. The solution of the sine-Gordon equation using the method of lines. Int. J. Comput. Math. 61 (1996) 271-292
2. Bratsos A.G. On the numerical solution of the Klein-Gordon equation. Numer. Methods Partial Differ. Equ. 25 (2009) 939-951
3. Bratsos A.G. A numerical method for the one-dimensional sine-Gordon equation. Numer. Methods Partial Differ. Equ. 24 (2008) 833-844
4. Caudrey P.J., Eilbeck I.C., and Gibbon J.D. The sine-Gordon equation as a model classical field theory. Nuovo Cimento 25 (1975) 497-511
5. Chui C.K. An Introduction to Wavelets (1992), Academic Press, San Diego, CA
6. Dodd R.K., Eilbeck I.C., Gibbon J.D., and Morris H.C. Solitons and Nonlinear Wave Equations (1982), Academic, London
7. de Boor C. A Practical Guide to Spline (1978), Springer-Verlag, New York
8. Deeba E.Y., and Khuri S.A. A decomposition method for solving the nonlinear Klein-Gordon equation. J. Comput. Phys. 124 (1996) 442-448
9. Dehghan M., and Shokri A. Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions. J. Comput. Appl. Math. 230 (2009) 400-410
10. Dehghan M., Mohebbi A., and Asghari Z. Fourth-order compact solution of the nonlinear Klein-Gordon equation. Numerical Algorithms 52 (2009) 523-540
11. Shakeri F., and Dehghan M. Numerical solution of the Klein-Gordon equation via He's variational iteration method. Nonlinear Dynamics 51 (2008) 89-97
12. Dehghan M. Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices. Math. Comput. Simulation 71 (2006) 16-30
13. Dehghan M. Parameter determination in a partial differential equation from the overspecified data. Math. Comput. Modelling 41 (2005) 196-213
14. Dehghan M. Efficient techniques for the second-order parabolic equation subject to nonlocal specifications. Appl. Numer. Math. 52 (2005) 39-62
15. Dehghan M. The one-dimensional heat equation subject to a boundary integral specification. Chaos Solitons Fractals 32 (2007) 661-675
16. Dehghan M. On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation. Numer. Methods Partial Differ. Equ. 21 (2005) 24-40
17. Dehghan M. Implicit collocation technique for heat equation with non-classic initial condition. Int. J. Nonlinear Sci. Numer. Simul. 7 (2006) 447-450
18. Dehghan M., and Ghesmati A. Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein-Gordon equation. Comput. Phys. Commun. 181 8 (2010) 1410-1418 this issue
19. Goswami J.C., and Chan A.K. Fundamentals of Wavelets, Theory, Algorithms, and Applications (1999), John Wiley & Sons, Inc.
20. Guo B.Y., Li X., and Vazquez L. A Legendre spectral method for solving the nonlinear Klein-Gordon equation. Math. Appl. Comput. 15 (1996) 19-36
21. Li X., and Guo B.Y. A Legendre spectral method for solving nonlinear Klein-Gordon equation. J. Comput. Math. 15 2 (1997) 105-126
22. Han H., and Zhang Z. Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domain. J. Comput. Phys. 227 (2008) 8992-9004
23. Dehghan M. A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications. Numer. Methods Partial Differ. Equ. 22 (2006) 220-257
24. Dehghan M. Identification of a time-dependent coefficient in a partial differential equation subject to an extra measurement. Numer. Methods Partial Differ. Equ. 21 (2005) 611-622
25. Khalifa M.E., and El-Gamal M. A numerical solution to Klein-Gordon equation with Dirichlet boundary condition. Appl. Math. Comput. 160 (2005) 451-475
26. Kaya D., and El-Sayed S.M. A numerical solution of the Klein-Gordon equation and convergence of the decomposition method. Appl. Math. Comput. 156 (2004) 341-353
27. El-Sayed S.M. The decomposition method for studying the Klein-Gordon equation. Chaos Solitons Fractals 18 (2003) 1025-1030
28. Ebaid A. Exact solutions for the generalized Klein-Gordon equation via a transformation and Exp-function method and comparison with Adomians' method. J. Comput. Appl. Math. 223 (2009) 278-290
29. Lynch M.A.M. Large amplitude instability in finite difference approximations to the Klein-Gordon equation. Appl. Numer. Math. 31 (1999) 173-182
30. Jiminez S., and Vazquez L. Analysis of four numerical schemes for a nonlinear Klein-Gordon equation. Appl. Math. Comput. 35 (1990) 61-94
31. Meyer Y. Ondelettes et Opérateurs, I: Ondelettes (1990), Hermann, Paris
32. Meyer Y. Ondelettes et Opérateurs, II: Opérateurs de Calderón-Zygmond (1990), Hermann, Paris
33. Meyer Y., and Coifman R. Ondelettes et Opérateurs, III: Opérateurs multilinéaires (1991), Hermann, Paris
34. Rashidinia J., and Mohammadi R. Tension spline approach for the numerical solution of nonlinear Klein-Gordon equation. Computer Physics Communications 181 (2010) 78-91
35. Wazwaz A.M. New travelling wave solutions to the Boussinesq and the Klein-Gordon equations. Commun. Nonlinear Sci. Numer. Simul. 13 (2008) 889-901
36. Sun Q. Solving the Klein-Gordon equation by means of the homotopy analysis method. Appl. Math. Comput. 169 (2005) 355-365
37. Wang Q.F., and Cheng D.Z. Numerical solution of damped nonlinear Klein-Gordon equations using variational iteration and finite element methods. Appl. Math. Comput. 162 (2005) 381-401
38. Wong Y.S., Chang Q., and Gong L. An initial-boundary value problem of a Klein-Gordon equation. Appl. Math. Comput. 84 (1997) 77-93
39. Wazwaz A.M. The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation. Appl. Math. Comput. 167 (2005) 1179-1195
40. Wazwaz A.M. The modified decomposition method for analytic treatment of differential equations. Appl. Math. Comput. 173 (2006) 165-176
41. Wazwaz A.M. Compactons, solitons and periodic solutions for some forms of nonlinear Klein-Gordon equations. Chaos Solitons Fractals 28 (2006) 1005-1013